Problem representation: The effects of spatial arrays

Abstract

Two studi.es exa~ined how characteristics of spatial arrays contribute to efficient problem representation. Thirty-two adults were presented with information about family relationships in one of two arrays: a hierarchy or a matrix. Their answers to two different sets of questions ere timed. The matrix format was superior to the hierarchy for one set of questions only; no differences between the arrays emerged for the other set. The data were interpreted in terms of how the family relationships were mapped onto the arrays; the mapping differences between the arrays affected the number of mental steps needed to solve some questions, but not others. In a second experiment (N=32), the same problem information was remapped onto the arrays, with the mapping relations reversed. As predicted, the pattern ofresponse times exactly reflected the change in mapping. It is proposed that, for spatial arrays, efficiency of problem representation is best understood in terms of the number of mental steps in the problem solution.

Evidence for abstract, schematic knowledge of three spatial diagram representations

“…e.g., Lynch, 1990;Winn, 1989), (2) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989), and (3) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991;Larkin & Simon, 1987). A number of studies provide empirical support for the benefits of using spatial diagram representations for learning and problem solving on specific tasks (e.g., Bartram, 1980;Carroll, Thomas, & Malhotra, 1980;Day, 1988;GuriRozenblit, 1988;McGuinness, 1986;Novick & Hmelo, 1994;S. H. Schwartz, 1971).…”

Tools for Representing Problems and the Knowledge Required to Solve Them

“…Because "problem solving must begin with the conversion of the problem statement into an internal representation" (Reimann & Chi, 1989, p. 165), and because individuals choose to represent problems in ways that make more sense to them. Problem spaces are mentally constructed by selecting and mapping specific relations from a problem domain onto the problem (McGuinness, 1986). These mappings may facilitate or impede different kinds of processing required to solve the problem.…”

Characteristics of a cognitive tool that helps students learn diagnostic problem solving

“…Drawing on research illustrating the connection between how individuals represent problems and their ability to solve them (e.g. Mayer, 1976;McGuinness, 1986;Pape & Tchoshanov, 2001;Zhang, 1997), Jonassen (2003) argued that cognitive tools (such as semantic network tools, expert systems shells, and systems modeling software) can promote learning of problem solving. The underlying premise is that people learn by constructing models/explanations of systems.…”